1.

Show that `f(x)=cos(2x+pi/4)`is an increasing function on `(3pi//8,7pi//8)dot`

Answer» given that `y= f(x)= cos(2x+pi/4)`
`dy/dx> 0 => -2sin(2x+pi/4)> 0`
`2sin(2x+ pi/4) <0`
`sinubrace(2x+ pi/4) < 0 `
`sin a < 0`so, `pi< a<2pi`
so must satisfy
`pi< 2x+pi/4<2pi`
`(3pi)/4 < 2x < (7pi)/4`
`(3pi)/8 < x < (7 pi)/8`
answer


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